Karlsson probably becomes a more marketable trade piece with only one year remaining because a trade can be worked out where the team acquiring him has a shot to talk an extension with him, and a realistic idea that Karlsson wants to be there long term. It'd have to be similar to the Spezza scenario where Karlsson let's them know a year out he isn't willing to talk about an extension and would accept a trade. (Let's hope it never gets to that).
The difference with Subban was that he was locked down long term at the time he was traded, so whoever acquired him he'd have to play for. That's why the Canadiens were in a rush to move him prior to his NTC kicking in.
If Karlsson walks away from the Sens, it'll be because he wants to go somewhere he thinks he can win, and he's decided Ottawa isn't a team he can win with. So to figure out what team might be a realistic destination you've gotta ask yourself who will be a contender by the 2018 off-season when Karl has 1 year left on his contract that will have a stock pile of assets they can move for Karlsson. Assuming he isn't scared of the cold, maybe Edmonton? Minnesota?
Teams like Toronto and Montreal asking about him are crazy, because there's no way Ottawa would trade arguably the biggest star in the history of their team within the division. What does Ottawa have to get back to justify that from Toronto even if Karlsson is walking as a UFA? Auston Matthews? Teams just don't do stuff like that.